LMFDB - Embedded newform 930.2.e.b.929.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(929,930)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("930.929");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.3
Character	$\chi$	$=$	930.929
Dual form			930.2.e.b.929.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.69795 - 0.341995i) q^{3} +1.00000 q^{4} +(1.23971 - 1.86095i) q^{5} +(-1.69795 - 0.341995i) q^{6} -0.843688i q^{7} +1.00000 q^{8} +(2.76608 + 1.16138i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.69795 - 0.341995i) q^{3} +1.00000 q^{4} +(1.23971 - 1.86095i) q^{5} +(-1.69795 - 0.341995i) q^{6} -0.843688i q^{7} +1.00000 q^{8} +(2.76608 + 1.16138i) q^{9} +(1.23971 - 1.86095i) q^{10} +2.73505 q^{11} +(-1.69795 - 0.341995i) q^{12} -1.61720 q^{13} -0.843688i q^{14} +(-2.74140 + 2.73583i) q^{15} +1.00000 q^{16} -3.82416i q^{17} +(2.76608 + 1.16138i) q^{18} -0.779676 q^{19} +(1.23971 - 1.86095i) q^{20} +(-0.288537 + 1.43254i) q^{21} +2.73505 q^{22} +3.42569i q^{23} +(-1.69795 - 0.341995i) q^{24} +(-1.92626 - 4.61406i) q^{25} -1.61720 q^{26} +(-4.29948 - 2.91795i) q^{27} -0.843688i q^{28} +4.68011 q^{29} +(-2.74140 + 2.73583i) q^{30} +(2.58461 - 4.93151i) q^{31} +1.00000 q^{32} +(-4.64398 - 0.935373i) q^{33} -3.82416i q^{34} +(-1.57006 - 1.04593i) q^{35} +(2.76608 + 1.16138i) q^{36} -4.77317 q^{37} -0.779676 q^{38} +(2.74592 + 0.553073i) q^{39} +(1.23971 - 1.86095i) q^{40} -7.71117i q^{41} +(-0.288537 + 1.43254i) q^{42} +6.37503 q^{43} +2.73505 q^{44} +(5.59040 - 3.70776i) q^{45} +3.42569i q^{46} -12.0004 q^{47} +(-1.69795 - 0.341995i) q^{48} +6.28819 q^{49} +(-1.92626 - 4.61406i) q^{50} +(-1.30784 + 6.49324i) q^{51} -1.61720 q^{52} -1.15264i q^{53} +(-4.29948 - 2.91795i) q^{54} +(3.39066 - 5.08979i) q^{55} -0.843688i q^{56} +(1.32385 + 0.266645i) q^{57} +4.68011 q^{58} +3.35056i q^{59} +(-2.74140 + 2.73583i) q^{60} -15.3049i q^{61} +(2.58461 - 4.93151i) q^{62} +(0.979844 - 2.33371i) q^{63} +1.00000 q^{64} +(-2.00485 + 3.00952i) q^{65} +(-4.64398 - 0.935373i) q^{66} -8.81399i q^{67} -3.82416i q^{68} +(1.17157 - 5.81666i) q^{69} +(-1.57006 - 1.04593i) q^{70} +13.6476i q^{71} +(2.76608 + 1.16138i) q^{72} +11.0551 q^{73} -4.77317 q^{74} +(1.69271 + 8.49322i) q^{75} -0.779676 q^{76} -2.30753i q^{77} +(2.74592 + 0.553073i) q^{78} +4.05329i q^{79} +(1.23971 - 1.86095i) q^{80} +(6.30239 + 6.42495i) q^{81} -7.71117i q^{82} +8.96229i q^{83} +(-0.288537 + 1.43254i) q^{84} +(-7.11657 - 4.74084i) q^{85} +6.37503 q^{86} +(-7.94659 - 1.60057i) q^{87} +2.73505 q^{88} -4.16066 q^{89} +(5.59040 - 3.70776i) q^{90} +1.36441i q^{91} +3.42569i q^{92} +(-6.07510 + 7.48954i) q^{93} -12.0004 q^{94} +(-0.966569 + 1.45094i) q^{95} +(-1.69795 - 0.341995i) q^{96} +0.560368i q^{97} +6.28819 q^{98} +(7.56537 + 3.17644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9	$ 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} + 4 q^{18} + 8 q^{19} - 2 q^{20} + 10 q^{25} - 12 q^{31} + 32 q^{32} + 8 q^{33} - 16 q^{35} + 4 q^{36} + 8 q^{38} - 4 q^{39} - 2 q^{40} - 42 q^{45} + 4 q^{47} - 36 q^{49} + 10 q^{50} - 4 q^{51} - 12 q^{62} + 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} + 4 q^{72} + 8 q^{76} - 4 q^{78} - 2 q^{80} + 24 q^{81} + 4 q^{87} - 42 q^{90} - 24 q^{93} + 4 q^{94} + 26 q^{95} - 36 q^{98}+O(q^{100}) $ 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 + 4 * q^18 + 8 * q^19 - 2 * q^20 + 10 * q^25 - 12 * q^31 + 32 * q^32 + 8 * q^33 - 16 * q^35 + 4 * q^36 + 8 * q^38 - 4 * q^39 - 2 * q^40 - 42 * q^45 + 4 * q^47 - 36 * q^49 + 10 * q^50 - 4 * q^51 - 12 * q^62 + 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 + 4 * q^72 + 8 * q^76 - 4 * q^78 - 2 * q^80 + 24 * q^81 + 4 * q^87 - 42 * q^90 - 24 * q^93 + 4 * q^94 + 26 * q^95 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.69795	−	0.341995i	−0.980313	−	0.197451i
$3$	−1.69795	−	0.341995i	−0.980313	−	0.197451i
$4$	1.00000			0.500000
$5$	1.23971	−	1.86095i	0.554413	−	0.832241i
$5$	1.23971	−	1.86095i	0.554413	−	0.832241i
$6$	−1.69795	−	0.341995i	−0.693186	−	0.139619i
$7$		−	0.843688i		−	0.318884i	−0.987207	−	0.159442i	$-0.949030\pi$
$7$		−	0.843688i		−	0.318884i	0.987207	−	0.159442i	$-0.0509695\pi$
$8$	1.00000			0.353553
$9$	2.76608	+	1.16138i	0.922026	+	0.387127i
$10$	1.23971	−	1.86095i	0.392030	−	0.588484i
$11$	2.73505			0.824649			0.412324	−	0.911037i	$-0.364717\pi$
$11$	2.73505			0.824649			0.412324	+	0.911037i	$0.364717\pi$
$12$	−1.69795	−	0.341995i	−0.490156	−	0.0987254i
$13$	−1.61720			−0.448530			−0.224265	−	0.974528i	$-0.571998\pi$
$13$	−1.61720			−0.448530			−0.224265	+	0.974528i	$0.571998\pi$
$14$		−	0.843688i		−	0.225485i
$15$	−2.74140	+	2.73583i	−0.707825	+	0.706387i
$16$	1.00000			0.250000
$17$		−	3.82416i		−	0.927495i	−0.885967	−	0.463748i	$-0.846504\pi$
$17$		−	3.82416i		−	0.927495i	0.885967	−	0.463748i	$-0.153496\pi$
$18$	2.76608	+	1.16138i	0.651971	+	0.273740i
$19$	−0.779676			−0.178870			−0.0894350	−	0.995993i	$-0.528506\pi$
$19$	−0.779676			−0.178870			−0.0894350	+	0.995993i	$0.528506\pi$
$20$	1.23971	−	1.86095i	0.277207	−	0.416121i
$21$	−0.288537	+	1.43254i	−0.0629640	+	0.312606i
$22$	2.73505			0.583115
$23$			3.42569i			0.714306i	0.934046	+	0.357153i	$0.116252\pi$
$23$			3.42569i			0.714306i	−0.934046	+	0.357153i	$0.883748\pi$
$24$	−1.69795	−	0.341995i	−0.346593	−	0.0698094i
$25$	−1.92626	−	4.61406i	−0.385251	−	0.922812i
$26$	−1.61720			−0.317159
$27$	−4.29948	−	2.91795i	−0.827436	−	0.561561i
$28$		−	0.843688i		−	0.159442i
$29$	4.68011			0.869074			0.434537	−	0.900654i	$-0.356912\pi$
$29$	4.68011			0.869074			0.434537	+	0.900654i	$0.356912\pi$
$30$	−2.74140	+	2.73583i	−0.500508	+	0.499491i
$31$	2.58461	−	4.93151i	0.464210	−	0.885725i
$31$	2.58461	−	4.93151i	0.464210	−	0.885725i
$32$	1.00000			0.176777
$33$	−4.64398	−	0.935373i	−0.808414	−	0.162828i
$34$		−	3.82416i		−	0.655838i
$35$	−1.57006	−	1.04593i	−0.265389	−	0.176794i
$36$	2.76608	+	1.16138i	0.461013	+	0.193564i
$37$	−4.77317			−0.784704			−0.392352	−	0.919815i	$-0.628338\pi$
$37$	−4.77317			−0.784704			−0.392352	+	0.919815i	$0.628338\pi$
$38$	−0.779676			−0.126480
$39$	2.74592	+	0.553073i	0.439700	+	0.0885626i
$40$	1.23971	−	1.86095i	0.196015	−	0.294242i
$41$		−	7.71117i		−	1.20428i	−0.798389	−	0.602142i	$-0.794314\pi$
$41$		−	7.71117i		−	1.20428i	0.798389	−	0.602142i	$-0.205686\pi$
$42$	−0.288537	+	1.43254i	−0.0445222	+	0.221046i
$43$	6.37503			0.972183			0.486092	−	0.873908i	$-0.338422\pi$
$43$	6.37503			0.972183			0.486092	+	0.873908i	$0.338422\pi$
$44$	2.73505			0.412324
$45$	5.59040	−	3.70776i	0.833367	−	0.552720i
$46$			3.42569i			0.505091i
$47$	−12.0004			−1.75043			−0.875216	−	0.483732i	$-0.839281\pi$
$47$	−12.0004			−1.75043			−0.875216	+	0.483732i	$0.839281\pi$
$48$	−1.69795	−	0.341995i	−0.245078	−	0.0493627i
$49$	6.28819			0.898313
$50$	−1.92626	−	4.61406i	−0.272414	−	0.652526i
$51$	−1.30784	+	6.49324i	−0.183135	+	0.909236i
$52$	−1.61720			−0.224265
$53$		−	1.15264i		−	0.158327i	−0.996862	−	0.0791637i	$-0.974775\pi$
$53$		−	1.15264i		−	0.158327i	0.996862	−	0.0791637i	$-0.0252250\pi$
$54$	−4.29948	−	2.91795i	−0.585085	−	0.397083i
$55$	3.39066	−	5.08979i	0.457196	−	0.686307i
$56$		−	0.843688i		−	0.112743i
$57$	1.32385	+	0.266645i	0.175349	+	0.0353180i
$58$	4.68011			0.614528
$59$			3.35056i			0.436206i	0.975926	+	0.218103i	$0.0699868\pi$
$59$			3.35056i			0.436206i	−0.975926	+	0.218103i	$0.930013\pi$
$60$	−2.74140	+	2.73583i	−0.353913	+	0.353194i
$61$		−	15.3049i		−	1.95959i	−0.199999	−	0.979796i	$-0.564094\pi$
$61$		−	15.3049i		−	1.95959i	0.199999	−	0.979796i	$-0.435906\pi$
$62$	2.58461	−	4.93151i	0.328246	−	0.626302i
$63$	0.979844	−	2.33371i	0.123449	−	0.294020i
$64$	1.00000			0.125000
$65$	−2.00485	+	3.00952i	−0.248671	+	0.373285i
$66$	−4.64398	−	0.935373i	−0.571635	−	0.115136i
$67$		−	8.81399i		−	1.07680i	−0.842689	−	0.538400i	$-0.819029\pi$
$67$		−	8.81399i		−	1.07680i	0.842689	−	0.538400i	$-0.180971\pi$
$68$		−	3.82416i		−	0.463748i
$69$	1.17157	−	5.81666i	0.141040	−	0.700243i
$70$	−1.57006	−	1.04593i	−0.187658	−	0.125012i
$71$			13.6476i			1.61967i	0.586655	+	0.809837i	$0.300444\pi$
$71$			13.6476i			1.61967i	−0.586655	+	0.809837i	$0.699556\pi$
$72$	2.76608	+	1.16138i	0.325986	+	0.136870i
$73$	11.0551			1.29391			0.646953	−	0.762530i	$-0.276043\pi$
$73$	11.0551			1.29391			0.646953	+	0.762530i	$0.276043\pi$
$74$	−4.77317			−0.554869
$75$	1.69271	+	8.49322i	0.195457	+	0.980712i
$76$	−0.779676			−0.0894350
$77$		−	2.30753i		−	0.262967i
$78$	2.74592	+	0.553073i	0.310915	+	0.0626232i
$79$			4.05329i			0.456030i	0.973658	+	0.228015i	$0.0732236\pi$
$79$			4.05329i			0.456030i	−0.973658	+	0.228015i	$0.926776\pi$
$80$	1.23971	−	1.86095i	0.138603	−	0.208060i
$81$	6.30239	+	6.42495i	0.700265	+	0.713883i
$82$		−	7.71117i		−	0.851557i
$83$			8.96229i			0.983740i	0.870669	+	0.491870i	$0.163686\pi$
$83$			8.96229i			0.983740i	−0.870669	+	0.491870i	$0.836314\pi$
$84$	−0.288537	+	1.43254i	−0.0314820	+	0.156303i
$85$	−7.11657	−	4.74084i	−0.771900	−	0.514216i
$86$	6.37503			0.687437
$87$	−7.94659	−	1.60057i	−0.851964	−	0.171599i
$88$	2.73505			0.291557
$89$	−4.16066			−0.441029			−0.220514	−	0.975384i	$-0.570774\pi$
$89$	−4.16066			−0.441029			−0.220514	+	0.975384i	$0.570774\pi$
$90$	5.59040	−	3.70776i	0.589279	−	0.390832i
$91$			1.36441i			0.143029i
$92$			3.42569i			0.357153i
$93$	−6.07510	+	7.48954i	−0.629958	+	0.776629i
$94$	−12.0004			−1.23774
$95$	−0.966569	+	1.45094i	−0.0991679	+	0.148863i
$96$	−1.69795	−	0.341995i	−0.173296	−	0.0349047i
$97$			0.560368i			0.0568967i	0.999595	+	0.0284484i	$0.00905662\pi$
$97$			0.560368i			0.0568967i	−0.999595	+	0.0284484i	$0.990943\pi$
$98$	6.28819			0.635203
$99$	7.56537	+	3.17644i	0.760348	+	0.319244i
$100$	−1.92626	−	4.61406i	−0.192626	−	0.461406i
$101$			15.7023i			1.56244i	0.624255	+	0.781221i	$0.285403\pi$
$101$			15.7023i			1.56244i	−0.624255	+	0.781221i	$0.714597\pi$
$102$	−1.30784	+	6.49324i	−0.129496	+	0.642927i
$103$			11.2232i			1.10585i	0.833230	+	0.552926i	$0.186489\pi$
$103$			11.2232i			1.10585i	−0.833230	+	0.552926i	$0.813511\pi$
$104$	−1.61720			−0.158579
$105$	2.30818	+	2.31288i	0.225256	+	0.225714i
$106$		−	1.15264i		−	0.111954i
$107$	−1.08405			−0.104799			−0.0523995	−	0.998626i	$-0.516687\pi$
$107$	−1.08405			−0.104799			−0.0523995	+	0.998626i	$0.516687\pi$
$108$	−4.29948	−	2.91795i	−0.413718	−	0.280780i
$109$	3.75581			0.359741			0.179871	−	0.983690i	$-0.442432\pi$
$109$	3.75581			0.359741			0.179871	+	0.983690i	$0.442432\pi$
$110$	3.39066	−	5.08979i	0.323287	−	0.485292i
$111$	8.10460	+	1.63240i	0.769255	+	0.154940i
$112$		−	0.843688i		−	0.0797210i
$113$	1.10003			0.103482			0.0517412	−	0.998661i	$-0.483523\pi$
$113$	1.10003			0.103482			0.0517412	+	0.998661i	$0.483523\pi$
$114$	1.32385	+	0.266645i	0.123990	+	0.0249736i
$115$	6.37503	+	4.24685i	0.594475	+	0.396021i
$116$	4.68011			0.434537
$117$	−4.47330	−	1.87818i	−0.413556	−	0.173638i
$118$			3.35056i			0.308444i
$119$	−3.22640			−0.295764
$120$	−2.74140	+	2.73583i	−0.250254	+	0.249746i
$121$	−3.51950			−0.319955
$122$		−	15.3049i		−	1.38564i
$123$	−2.63718	+	13.0932i	−0.237787	+	1.18057i
$124$	2.58461	−	4.93151i	0.232105	−	0.442863i
$125$	−10.9745	−	2.13541i	−0.981591	−	0.190997i
$126$	0.979844	−	2.33371i	0.0872914	−	0.207903i
$127$	5.67746			0.503793			0.251896	−	0.967754i	$-0.418946\pi$
$127$	5.67746			0.503793			0.251896	+	0.967754i	$0.418946\pi$
$128$	1.00000			0.0883883
$129$	−10.8245	−	2.18023i	−0.953044	−	0.191958i
$130$	−2.00485	+	3.00952i	−0.175837	+	0.263952i
$131$			4.21104i			0.367920i	0.982934	+	0.183960i	$0.0588918\pi$
$131$			4.21104i			0.367920i	−0.982934	+	0.183960i	$0.941108\pi$
$132$	−4.64398	−	0.935373i	−0.404207	−	0.0814138i
$133$			0.657804i			0.0570388i
$134$		−	8.81399i		−	0.761413i
$135$	−10.7603	+	4.38371i	−0.926095	+	0.377289i
$136$		−	3.82416i		−	0.327919i
$137$			4.53024i			0.387045i	0.981096	+	0.193522i	$0.0619912\pi$
$137$			4.53024i			0.387045i	−0.981096	+	0.193522i	$0.938009\pi$
$138$	1.17157	−	5.81666i	0.0997305	−	0.495147i
$139$			4.60841i			0.390880i	0.980716	+	0.195440i	$0.0626135\pi$
$139$			4.60841i			0.390880i	−0.980716	+	0.195440i	$0.937386\pi$
$140$	−1.57006	−	1.04593i	−0.132694	−	0.0883968i
$141$	20.3760	+	4.10406i	1.71597	+	0.345624i
$142$			13.6476i			1.14528i
$143$	−4.42312			−0.369880
$144$	2.76608	+	1.16138i	0.230507	+	0.0967818i
$145$	5.80196	−	8.70944i	0.481826	−	0.723279i
$146$	11.0551			0.914930
$147$	−10.6770	−	2.15053i	−0.880628	−	0.177373i
$148$	−4.77317			−0.392352
$149$		−	9.92239i		−	0.812874i	−0.913679	−	0.406437i	$-0.866771\pi$
$149$		−	9.92239i		−	0.812874i	0.913679	−	0.406437i	$-0.133229\pi$
$150$	1.69271	+	8.49322i	0.138209	+	0.693468i
$151$			8.00263i			0.651244i	0.945500	+	0.325622i	$0.105574\pi$
$151$			8.00263i			0.651244i	−0.945500	+	0.325622i	$0.894426\pi$
$152$	−0.779676			−0.0632401
$153$	4.44131	−	10.5779i	0.359059	−	0.855175i
$154$		−	2.30753i		−	0.185946i
$155$	−5.97313	−	10.9235i	−0.479773	−	0.877393i
$156$	2.74592	+	0.553073i	0.219850	+	0.0442813i
$157$		−	3.59827i		−	0.287173i	−0.989638	−	0.143586i	$-0.954136\pi$
$157$		−	3.59827i		−	0.287173i	0.989638	−	0.143586i	$-0.0458635\pi$
$158$			4.05329i			0.322462i
$159$	−0.394197	+	1.95713i	−0.0312619	+	0.155210i
$160$	1.23971	−	1.86095i	0.0980074	−	0.147121i
$161$	2.89021			0.227781
$162$	6.30239	+	6.42495i	0.495162	+	0.504791i
$163$		−	5.86145i		−	0.459104i	−0.973296	−	0.229552i	$-0.926274\pi$
$163$		−	5.86145i		−	0.459104i	0.973296	−	0.229552i	$-0.0737261\pi$
$164$		−	7.71117i		−	0.602142i
$165$	−7.49786	+	7.48262i	−0.583707	+	0.582521i
$166$			8.96229i			0.695609i
$167$			18.7631i			1.45193i	0.687730	+	0.725966i	$0.258607\pi$
$167$			18.7631i			1.45193i	−0.687730	+	0.725966i	$0.741393\pi$
$168$	−0.288537	+	1.43254i	−0.0222611	+	0.110523i
$169$	−10.3847			−0.798821
$170$	−7.11657	−	4.74084i	−0.545816	−	0.363606i
$171$	−2.15665	−	0.905502i	−0.164923	−	0.0692454i
$172$	6.37503			0.486092
$173$	12.4976			0.950175			0.475087	−	0.879939i	$-0.342416\pi$
$173$	12.4976			0.950175			0.475087	+	0.879939i	$0.342416\pi$
$174$	−7.94659	−	1.60057i	−0.602430	−	0.121339i
$175$	−3.89283	+	1.62516i	−0.294270	+	0.122851i
$176$	2.73505			0.206162
$177$	1.14587	−	5.68909i	0.0861292	−	0.427618i
$178$	−4.16066			−0.311854
$179$	−13.9995			−1.04637			−0.523187	−	0.852218i	$-0.675257\pi$
$179$	−13.9995			−1.04637			−0.523187	+	0.852218i	$0.675257\pi$
$180$	5.59040	−	3.70776i	0.416684	−	0.276360i
$181$			12.4546i			0.925743i	0.886425	+	0.462871i	$0.153181\pi$
$181$			12.4546i			0.925743i	−0.886425	+	0.462871i	$0.846819\pi$
$182$			1.36441i			0.101137i
$183$	−5.23420	+	25.9870i	−0.386923	+	1.92101i
$184$			3.42569i			0.252545i
$185$	−5.91732	+	8.88262i	−0.435050	+	0.653063i
$186$	−6.07510	+	7.48954i	−0.445448	+	0.549160i
$187$		−	10.4593i		−	0.764858i
$188$	−12.0004			−0.875216
$189$	−2.46184	+	3.62742i	−0.179073	+	0.263856i
$190$	−0.966569	+	1.45094i	−0.0701223	+	0.105262i
$191$			15.2090i			1.10048i	0.835006	+	0.550241i	$0.185464\pi$
$191$			15.2090i			1.10048i	−0.835006	+	0.550241i	$0.814536\pi$
$192$	−1.69795	−	0.341995i	−0.122539	−	0.0246814i
$193$			16.9683i			1.22141i	0.791859	+	0.610704i	$0.209113\pi$
$193$			16.9683i			1.22141i	−0.791859	+	0.610704i	$0.790887\pi$
$194$			0.560368i			0.0402321i
$195$	4.43338	−	4.42437i	0.317481	−	0.316836i
$196$	6.28819			0.449156
$197$			0.0276191i			0.00196778i	1.00000		0.000983889i	$0.000313182\pi$
$197$			0.0276191i			0.00196778i	−1.00000		0.000983889i	$0.999687\pi$
$198$	7.56537	+	3.17644i	0.537647	+	0.225740i
$199$			11.5441i			0.818342i	0.912458	+	0.409171i	$0.134182\pi$
$199$			11.5441i			0.818342i	−0.912458	+	0.409171i	$0.865818\pi$
$200$	−1.92626	−	4.61406i	−0.136207	−	0.326263i
$201$	−3.01434	+	14.9657i	−0.212615	+	1.05560i
$202$			15.7023i			1.10481i
$203$		−	3.94855i		−	0.277134i
$204$	−1.30784	+	6.49324i	−0.0915674	+	0.454618i
$205$	−14.3501	−	9.55959i	−1.00225	−	0.667671i
$206$			11.2232i			0.781956i
$207$	−3.97853	+	9.47573i	−0.276527	+	0.658609i
$208$	−1.61720			−0.112132
$209$	−2.13245			−0.147505
$210$	2.30818	+	2.31288i	0.159280	+	0.159604i
$211$	−18.1486			−1.24940			−0.624701	−	0.780864i	$-0.714779\pi$
$211$	−18.1486			−1.24940			−0.624701	+	0.780864i	$0.714779\pi$
$212$		−	1.15264i		−	0.0791637i
$213$	4.66741	−	23.1730i	0.319806	−	1.58779i
$214$	−1.08405			−0.0741040
$215$	7.90317	−	11.8636i	0.538992	−	0.809091i
$216$	−4.29948	−	2.91795i	−0.292543	−	0.198542i
$217$	−4.16066	−	2.18061i	−0.282444	−	0.148029i
$218$	3.75581			0.254375
$219$	−18.7711	−	3.78080i	−1.26843	−	0.255483i
$220$	3.39066	−	5.08979i	0.228598	−	0.343153i
$221$			6.18442i			0.416009i
$222$	8.10460	+	1.63240i	0.543945	+	0.109559i
$223$	17.9289			1.20061			0.600303	−	0.799773i	$-0.295047\pi$
$223$	17.9289			1.20061			0.600303	+	0.799773i	$0.295047\pi$
$224$		−	0.843688i		−	0.0563713i
$225$	0.0305023	−	15.0000i	0.00203349	−	0.999998i
$226$	1.10003			0.0731731
$227$	0.176461			0.0117121			0.00585607	−	0.999983i	$-0.498136\pi$
$227$	0.176461			0.0117121			0.00585607	+	0.999983i	$0.498136\pi$
$228$	1.32385	+	0.266645i	0.0876743	+	0.0176590i
$229$			11.0643i			0.731152i	0.930781	+	0.365576i	$0.119128\pi$
$229$			11.0643i			0.731152i	−0.930781	+	0.365576i	$0.880872\pi$
$230$	6.37503	+	4.24685i	0.420357	+	0.280029i
$231$	−0.789163	+	3.91807i	−0.0519231	+	0.257790i
$232$	4.68011			0.307264
$233$	24.2221			1.58684			0.793421	−	0.608673i	$-0.208298\pi$
$233$	24.2221			1.58684			0.793421	+	0.608673i	$0.208298\pi$
$234$	−4.47330	−	1.87818i	−0.292428	−	0.122781i
$235$	−14.8769	+	22.3320i	−0.970463	+	1.45678i
$236$			3.35056i			0.218103i
$237$	1.38620	−	6.88228i	0.0900436	−	0.447052i
$238$	−3.22640			−0.209136
$239$	17.6019			1.13857			0.569287	−	0.822139i	$-0.307219\pi$
$239$	17.6019			1.13857			0.569287	+	0.822139i	$0.307219\pi$
$240$	−2.74140	+	2.73583i	−0.176956	+	0.176597i
$241$			2.08146i			0.134079i	0.997750	+	0.0670393i	$0.0213553\pi$
$241$			2.08146i			0.134079i	−0.997750	+	0.0670393i	$0.978645\pi$
$242$	−3.51950			−0.226242
$243$	−8.50385	−	13.0646i	−0.545522	−	0.838096i
$244$		−	15.3049i		−	0.979796i
$245$	7.79551	−	11.7020i	0.498037	−	0.747613i
$246$	−2.63718	+	13.0932i	−0.168141	+	0.834792i
$247$	1.26089			0.0802285
$248$	2.58461	−	4.93151i	0.164123	−	0.313151i
$249$	3.06506	−	15.2175i	0.194240	−	0.964372i
$250$	−10.9745	−	2.13541i	−0.694089	−	0.135055i
$251$	7.08567			0.447243			0.223622	−	0.974676i	$-0.428212\pi$
$251$	7.08567			0.447243			0.223622	+	0.974676i	$0.428212\pi$
$252$	0.979844	−	2.33371i	0.0617244	−	0.147010i
$253$			9.36944i			0.589051i
$254$	5.67746			0.356235
$255$	10.4622	+	10.4835i	0.655171	+	0.656505i
$256$	1.00000			0.0625000
$257$	22.8921			1.42797			0.713985	−	0.700161i	$-0.246888\pi$
$257$	22.8921			1.42797			0.713985	+	0.700161i	$0.246888\pi$
$258$	−10.8245	−	2.18023i	−0.673904	−	0.135735i
$259$			4.02706i			0.250230i
$260$	−2.00485	+	3.00952i	−0.124335	+	0.186643i
$261$	12.9455	+	5.43539i	0.801309	+	0.336442i
$262$			4.21104i			0.260159i
$263$			19.3207i			1.19136i	0.803221	+	0.595681i	$0.203118\pi$
$263$			19.3207i			1.19136i	−0.803221	+	0.595681i	$0.796882\pi$
$264$	−4.64398	−	0.935373i	−0.285817	−	0.0575682i
$265$	−2.14501	−	1.42894i	−0.131767	−	0.0877789i
$266$			0.657804i			0.0403325i
$267$	7.06459	+	1.42292i	0.432346	+	0.0870815i
$268$		−	8.81399i		−	0.538400i
$269$	−21.6216			−1.31829			−0.659145	−	0.752016i	$-0.729082\pi$
$269$	−21.6216			−1.31829			−0.659145	+	0.752016i	$0.729082\pi$
$270$	−10.7603	+	4.38371i	−0.654848	+	0.266784i
$271$		−	26.2479i		−	1.59445i	−0.603684	−	0.797223i	$-0.706301\pi$
$271$		−	26.2479i		−	1.59445i	0.603684	−	0.797223i	$-0.293699\pi$
$272$		−	3.82416i		−	0.231874i
$273$	0.466621	−	2.31670i	0.0282412	−	0.140213i
$274$			4.53024i			0.273682i
$275$	−5.26841	−	12.6197i	−0.317697	−	0.760995i
$276$	1.17157	−	5.81666i	0.0705201	−	0.350122i
$277$	21.4548			1.28910			0.644548	−	0.764564i	$-0.277046\pi$
$277$	21.4548			1.28910			0.644548	+	0.764564i	$0.277046\pi$
$278$			4.60841i			0.276394i
$279$	12.8766	−	10.6392i	0.770902	−	0.636954i
$280$	−1.57006	−	1.04593i	−0.0938290	−	0.0625060i
$281$			4.95539i			0.295614i	0.989016	+	0.147807i	$0.0472214\pi$
$281$			4.95539i			0.295614i	−0.989016	+	0.147807i	$0.952779\pi$
$282$	20.3760	+	4.10406i	1.21337	+	0.244393i
$283$		−	28.4636i		−	1.69199i	−0.533192	−	0.845994i	$-0.679008\pi$
$283$		−	28.4636i		−	1.69199i	0.533192	−	0.845994i	$-0.320992\pi$
$284$			13.6476i			0.809837i
$285$	2.13740	−	2.13306i	0.126609	−	0.126352i
$286$	−4.42312			−0.261544
$287$	−6.50583			−0.384027
$288$	2.76608	+	1.16138i	0.162993	+	0.0684351i
$289$	2.37579			0.139752
$290$	5.80196	−	8.70944i	0.340703	−	0.511436i
$291$	0.191643	−	0.951477i	0.0112343	−	0.0557766i
$292$	11.0551			0.646953
$293$	−11.1227			−0.649792			−0.324896	−	0.945750i	$-0.605329\pi$
$293$	−11.1227			−0.649792			−0.324896	+	0.945750i	$0.605329\pi$
$294$	−10.6770	−	2.15053i	−0.622698	−	0.125421i
$295$	6.23522	+	4.15371i	0.363029	+	0.241838i
$296$	−4.77317			−0.277435
$297$	−11.7593	−	7.98075i	−0.682344	−	0.463090i
$298$		−	9.92239i		−	0.574789i
$299$		−	5.54002i		−	0.320388i
$300$	1.69271	+	8.49322i	0.0977285	+	0.490356i
$301$		−	5.37854i		−	0.310014i
$302$			8.00263i			0.460499i
$303$	5.37012	−	26.6618i	0.308505	−	1.53168i
$304$	−0.779676			−0.0447175
$305$	−28.4816	−	18.9736i	−1.63085	−	1.08642i
$306$	4.44131	−	10.5779i	0.253893	−	0.604700i
$307$		−	1.52502i		−	0.0870373i	−0.999053	−	0.0435187i	$-0.986143\pi$
$307$		−	1.52502i		−	0.0870373i	0.999053	−	0.0435187i	$-0.0138568\pi$
$308$		−	2.30753i		−	0.131484i
$309$	3.83827	−	19.0564i	0.218352	−	1.08408i
$310$	−5.97313	−	10.9235i	−0.339251	−	0.620410i
$311$			9.63822i			0.546533i	0.961938	+	0.273267i	$0.0881041\pi$
$311$			9.63822i			0.546533i	−0.961938	+	0.273267i	$0.911896\pi$
$312$	2.74592	+	0.553073i	0.155457	+	0.0313116i
$313$	1.15835			0.0654739			0.0327370	−	0.999464i	$-0.489578\pi$
$313$	1.15835			0.0654739			0.0327370	+	0.999464i	$0.489578\pi$
$314$		−	3.59827i		−	0.203062i
$315$	−3.12819	−	4.71655i	−0.176254	−	0.265748i
$316$			4.05329i			0.228015i
$317$	28.4993			1.60068			0.800341	−	0.599545i	$-0.204652\pi$
$317$	28.4993			1.60068			0.800341	+	0.599545i	$0.204652\pi$
$318$	−0.394197	+	1.95713i	−0.0221055	+	0.109750i
$319$	12.8003			0.716681
$320$	1.23971	−	1.86095i	0.0693017	−	0.104030i
$321$	1.84066	+	0.370739i	0.102736	+	0.0206926i
$322$	2.89021			0.161065
$323$			2.98161i			0.165901i
$324$	6.30239	+	6.42495i	0.350133	+	0.356941i
$325$	3.11514	+	7.46184i	0.172797	+	0.413909i
$326$		−	5.86145i		−	0.324635i
$327$	−6.37718	−	1.28447i	−0.352659	−	0.0710312i
$328$		−	7.71117i		−	0.425778i
$329$			10.1246i			0.558185i
$330$	−7.49786	+	7.48262i	−0.412743	+	0.411905i
$331$		−	24.7211i		−	1.35880i	−0.733769	−	0.679399i	$-0.762241\pi$
$331$		−	24.7211i		−	1.35880i	0.733769	−	0.679399i	$-0.237759\pi$
$332$			8.96229i			0.491870i
$333$	−13.2030	−	5.54347i	−0.723517	−	0.303780i
$334$			18.7631i			1.02667i
$335$	−16.4024	−	10.9268i	−0.896158	−	0.596993i
$336$	−0.288537	+	1.43254i	−0.0157410	+	0.0781516i
$337$	−21.0103			−1.14450			−0.572251	−	0.820079i	$-0.693930\pi$
$337$	−21.0103			−1.14450			−0.572251	+	0.820079i	$0.693930\pi$
$338$	−10.3847			−0.564852
$339$	−1.86780	−	0.376206i	−0.101445	−	0.0204327i
$340$	−7.11657	−	4.74084i	−0.385950	−	0.257108i
$341$	7.06904	−	13.4879i	0.382810	−	0.730412i
$342$	−2.15665	−	0.905502i	−0.116618	−	0.0489639i
$343$		−	11.2111i		−	0.605342i
$344$	6.37503			0.343719
$345$	−9.37210	−	9.39117i	−0.504577	−	0.505604i
$346$	12.4976			0.671875
$347$		−	0.887639i		−	0.0476510i	−0.999716	−	0.0238255i	$-0.992415\pi$
$347$		−	0.887639i		−	0.0476510i	0.999716	−	0.0238255i	$-0.00758460\pi$
$348$	−7.94659	−	1.60057i	−0.425982	−	0.0857997i
$349$	−15.6359			−0.836969			−0.418485	−	0.908224i	$-0.637439\pi$
$349$	−15.6359			−0.836969			−0.418485	+	0.908224i	$0.637439\pi$
$350$	−3.89283	+	1.62516i	−0.208080	+	0.0868685i
$351$	6.95311	+	4.71891i	0.371130	+	0.251877i
$352$	2.73505			0.145779
$353$			28.4457i			1.51401i	0.653409	+	0.757005i	$0.273338\pi$
$353$			28.4457i			1.51401i	−0.653409	+	0.757005i	$0.726662\pi$
$354$	1.14587	−	5.68909i	0.0609025	−	0.302372i
$355$	25.3975	+	16.9190i	1.34796	+	0.897969i
$356$	−4.16066			−0.220514
$357$	5.47827	+	1.10341i	0.289941	+	0.0583988i
$358$	−13.9995			−0.739899
$359$		−	19.6674i		−	1.03801i	−0.854772	−	0.519003i	$-0.826303\pi$
$359$		−	19.6674i		−	1.03801i	0.854772	−	0.519003i	$-0.173697\pi$
$360$	5.59040	−	3.70776i	0.294640	−	0.195416i
$361$	−18.3921			−0.968006
$362$			12.4546i			0.654599i
$363$	5.97594	+	1.20365i	0.313656	+	0.0631753i
$364$			1.36441i			0.0715145i
$365$	13.7051	−	20.5730i	0.717359	−	1.07684i
$366$	−5.23420	+	25.9870i	−0.273596	+	1.35836i
$367$	11.1028			0.579563			0.289782	−	0.957093i	$-0.406417\pi$
$367$	11.1028			0.579563			0.289782	+	0.957093i	$0.406417\pi$
$368$			3.42569i			0.178576i
$369$	8.95561	−	21.3297i	0.466211	−	1.11038i
$370$	−5.91732	+	8.88262i	−0.307627	+	0.461785i
$371$	−0.972470			−0.0504881
$372$	−6.07510	+	7.48954i	−0.314979	+	0.388315i
$373$			9.10716i			0.471551i	0.971808	+	0.235775i	$0.0757629\pi$
$373$			9.10716i			0.471551i	−0.971808	+	0.235775i	$0.924237\pi$
$374$		−	10.4593i		−	0.540836i
$375$	17.9039	+	7.37905i	0.924553	+	0.381053i
$376$	−12.0004			−0.618871
$377$	−7.56866			−0.389806
$378$	−2.46184	+	3.62742i	−0.126624	+	0.186574i
$379$	16.6992			0.857779			0.428890	−	0.903357i	$-0.358905\pi$
$379$	16.6992			0.857779			0.428890	+	0.903357i	$0.358905\pi$
$380$	−0.966569	+	1.45094i	−0.0495840	+	0.0744315i
$381$	−9.64005	−	1.94166i	−0.493875	−	0.0994743i
$382$			15.2090i			0.778158i
$383$			2.67292i			0.136580i	0.997666	+	0.0682898i	$0.0217543\pi$
$383$			2.67292i			0.136580i	−0.997666	+	0.0682898i	$0.978246\pi$
$384$	−1.69795	−	0.341995i	−0.0866482	−	0.0174524i
$385$	−4.29419	−	2.86066i	−0.218852	−	0.145793i
$386$			16.9683i			0.863666i
$387$	17.6338	+	7.40385i	0.896379	+	0.376359i
$388$			0.560368i			0.0284484i
$389$	−4.87027			−0.246932			−0.123466	−	0.992349i	$-0.539401\pi$
$389$	−4.87027			−0.246932			−0.123466	+	0.992349i	$0.539401\pi$
$390$	4.43338	−	4.42437i	0.224493	−	0.224037i
$391$	13.1004			0.662515
$392$	6.28819			0.317602
$393$	1.44015	−	7.15014i	0.0726462	−	0.360677i
$394$			0.0276191i			0.00139143i
$395$	7.54296	+	5.02488i	0.379527	+	0.252829i
$396$	7.56537	+	3.17644i	0.380174	+	0.159622i
$397$		−	30.4343i		−	1.52746i	−0.645538	−	0.763728i	$-0.723367\pi$
$397$		−	30.4343i		−	1.52746i	0.645538	−	0.763728i	$-0.276633\pi$
$398$			11.5441i			0.578655i
$399$	0.224965	−	1.11692i	0.0112624	−	0.0559159i
$400$	−1.92626	−	4.61406i	−0.0963129	−	0.230703i
$401$	−6.28004			−0.313610			−0.156805	−	0.987630i	$-0.550119\pi$
$401$	−6.28004			−0.313610			−0.156805	+	0.987630i	$0.550119\pi$
$402$	−3.01434	+	14.9657i	−0.150342	+	0.746423i
$403$	−4.17983	+	7.97522i	−0.208212	+	0.397274i
$404$			15.7023i			0.781221i
$405$	19.7696	−	3.76337i	0.982359	−	0.187003i
$406$		−	3.94855i		−	0.195963i
$407$	−13.0548			−0.647105
$408$	−1.30784	+	6.49324i	−0.0647479	+	0.321463i
$409$		−	0.893121i		−	0.0441620i	−0.999756	−	0.0220810i	$-0.992971\pi$
$409$		−	0.893121i		−	0.0441620i	0.999756	−	0.0220810i	$-0.00702917\pi$
$410$	−14.3501	−	9.55959i	−0.708701	−	0.472114i
$411$	1.54932	−	7.69213i	0.0764223	−	0.379425i
$412$			11.2232i			0.552926i
$413$	2.82683			0.139099
$414$	−3.97853	+	9.47573i	−0.195534	+	0.465707i
$415$	16.6784	+	11.1106i	0.818709	+	0.545398i
$416$	−1.61720			−0.0792896
$417$	1.57605	−	7.82486i	0.0771797	−	0.383185i
$418$	−2.13245			−0.104302
$419$		−	8.98602i		−	0.438996i	−0.975613	−	0.219498i	$-0.929558\pi$
$419$		−	8.98602i		−	0.438996i	0.975613	−	0.219498i	$-0.0704419\pi$
$420$	2.30818	+	2.31288i	0.112628	+	0.112857i
$421$	25.5348			1.24449			0.622244	−	0.782823i	$-0.286221\pi$
$421$	25.5348			1.24449			0.622244	+	0.782823i	$0.286221\pi$
$422$	−18.1486			−0.883461
$423$	−33.1939	−	13.9370i	−1.61394	−	0.677640i
$424$		−	1.15264i		−	0.0559772i
$425$	−17.6449	+	7.36632i	−0.855904	+	0.357319i
$426$	4.66741	−	23.1730i	0.226137	−	1.12274i
$427$	−12.9126			−0.624883
$428$	−1.08405			−0.0523995
$429$	7.51024	+	1.51268i	0.362598	+	0.0730330i
$430$	7.90317	−	11.8636i	0.381125	−	0.572114i
$431$			14.8006i			0.712918i	0.934311	+	0.356459i	$0.116016\pi$
$431$			14.8006i			0.712918i	−0.934311	+	0.356459i	$0.883984\pi$
$432$	−4.29948	−	2.91795i	−0.206859	−	0.140390i
$433$	−29.4170			−1.41369			−0.706846	−	0.707367i	$-0.749883\pi$
$433$	−29.4170			−1.41369			−0.706846	+	0.707367i	$0.749883\pi$
$434$	−4.16066	−	2.18061i	−0.199718	−	0.104672i
$435$	−12.8300	+	12.8040i	−0.615153	+	0.613903i
$436$	3.75581			0.179871
$437$		−	2.67093i		−	0.127768i
$438$	−18.7711	−	3.78080i	−0.896917	−	0.180654i
$439$	19.6199			0.936406			0.468203	−	0.883621i	$-0.344902\pi$
$439$	19.6199			0.936406			0.468203	+	0.883621i	$0.344902\pi$
$440$	3.39066	−	5.08979i	0.161643	−	0.242646i
$441$	17.3936	+	7.30299i	0.828268	+	0.347761i
$442$			6.18442i			0.294163i
$443$	3.60874			0.171457			0.0857283	−	0.996319i	$-0.472678\pi$
$443$	3.60874			0.171457			0.0857283	+	0.996319i	$0.472678\pi$
$444$	8.10460	+	1.63240i	0.384628	+	0.0774702i
$445$	−5.15799	+	7.74277i	−0.244512	+	0.367042i
$446$	17.9289			0.848957
$447$	−3.39341	+	16.8477i	−0.160503	+	0.796871i
$448$		−	0.843688i		−	0.0398605i
$449$	2.43366			0.114852			0.0574258	−	0.998350i	$-0.481711\pi$
$449$	2.43366			0.114852			0.0574258	+	0.998350i	$0.481711\pi$
$450$	0.0305023	−	15.0000i	0.00143789	−	0.707105i
$451$		−	21.0904i		−	0.993110i
$452$	1.10003			0.0517412
$453$	2.73686	−	13.5881i	0.128589	−	0.638423i
$454$	0.176461			0.00828174
$455$	2.53910	+	1.69147i	0.119035	+	0.0792972i
$456$	1.32385	+	0.266645i	0.0619951	+	0.0124868i
$457$	−3.07246			−0.143724			−0.0718618	−	0.997415i	$-0.522894\pi$
$457$	−3.07246			−0.143724			−0.0718618	+	0.997415i	$0.522894\pi$
$458$			11.0643i			0.517003i
$459$	−11.1587	+	16.4419i	−0.520845	+	0.767443i
$460$	6.37503	+	4.24685i	0.297237	+	0.198010i
$461$	−33.4920			−1.55988			−0.779939	−	0.625856i	$-0.784750\pi$
$461$	−33.4920			−1.55988			−0.779939	+	0.625856i	$0.784750\pi$
$462$	−0.789163	+	3.91807i	−0.0367152	+	0.182285i
$463$	−21.3313			−0.991349			−0.495674	−	0.868508i	$-0.665079\pi$
$463$	−21.3313			−0.991349			−0.495674	+	0.868508i	$0.665079\pi$
$464$	4.68011			0.217268
$465$	6.40631	+	20.5903i	0.297086	+	0.954851i
$466$	24.2221			1.12207
$467$	−4.43260			−0.205116			−0.102558	−	0.994727i	$-0.532703\pi$
$467$	−4.43260			−0.205116			−0.102558	+	0.994727i	$0.532703\pi$
$468$	−4.47330	−	1.87818i	−0.206778	−	0.0868191i
$469$	−7.43626			−0.343375
$470$	−14.8769	+	22.3320i	−0.686221	+	1.03010i
$471$	−1.23059	+	6.10968i	−0.0567025	+	0.281519i
$472$			3.35056i			0.154222i
$473$	17.4360			0.801710
$474$	1.38620	−	6.88228i	0.0636704	−	0.316114i
$475$	1.50186	+	3.59747i	0.0689099	+	0.165063i
$476$	−3.22640			−0.147882
$477$	1.33866	−	3.18830i	0.0612929	−	0.145982i
$478$	17.6019			0.805094
$479$			3.79781i			0.173526i	0.996229	+	0.0867632i	$0.0276523\pi$
$479$			3.79781i			0.173526i	−0.996229	+	0.0867632i	$0.972348\pi$
$480$	−2.74140	+	2.73583i	−0.125127	+	0.124873i
$481$	7.71915			0.351963
$482$			2.08146i			0.0948078i
$483$	−4.90744	−	0.988439i	−0.223296	−	0.0449755i
$484$	−3.51950			−0.159977
$485$	1.04282	+	0.694691i	0.0473518	+	0.0315443i
$486$	−8.50385	−	13.0646i	−0.385742	−	0.592624i
$487$	−19.3169			−0.875332			−0.437666	−	0.899138i	$-0.644195\pi$
$487$	−19.3169			−0.875332			−0.437666	+	0.899138i	$0.644195\pi$
$488$		−	15.3049i		−	0.692820i
$489$	−2.00458	+	9.95245i	−0.0906504	+	0.450065i
$490$	7.79551	−	11.7020i	0.352165	−	0.528642i
$491$	4.82700			0.217840			0.108920	−	0.994051i	$-0.465261\pi$
$491$	4.82700			0.217840			0.108920	+	0.994051i	$0.465261\pi$
$492$	−2.63718	+	13.0932i	−0.118893	+	0.590287i
$493$		−	17.8975i		−	0.806062i
$494$	1.26089			0.0567301
$495$	15.2900	−	10.1409i	0.687235	−	0.455800i
$496$	2.58461	−	4.93151i	0.116052	−	0.221431i
$497$	11.5143			0.516488
$498$	3.06506	−	15.2175i	0.137349	−	0.681914i
$499$			43.7159i			1.95699i	0.206266	+	0.978496i	$0.433869\pi$
$499$			43.7159i			1.95699i	−0.206266	+	0.978496i	$0.566131\pi$
$500$	−10.9745	−	2.13541i	−0.490795	−	0.0954985i
$501$	6.41689	−	31.8588i	0.286685	−	1.42335i
$502$	7.08567			0.316249
$503$	−1.21923			−0.0543626			−0.0271813	−	0.999631i	$-0.508653\pi$
$503$	−1.21923			−0.0543626			−0.0271813	+	0.999631i	$0.508653\pi$
$504$	0.979844	−	2.33371i	0.0436457	−	0.103952i
$505$	29.2212	+	19.4663i	1.30033	+	0.866238i
$506$			9.36944i			0.416522i
$507$	17.6327	+	3.55150i	0.783094	+	0.157728i
$508$	5.67746			0.251896
$509$	−2.86789			−0.127117			−0.0635584	−	0.997978i	$-0.520245\pi$
$509$	−2.86789			−0.127117			−0.0635584	+	0.997978i	$0.520245\pi$
$510$	10.4622	+	10.4835i	0.463276	+	0.464219i
$511$		−	9.32709i		−	0.412606i
$512$	1.00000			0.0441942
$513$	3.35220	+	2.27506i	0.148003	+	0.100446i
$514$	22.8921			1.00973
$515$	20.8858	+	13.9134i	0.920336	+	0.613099i
$516$	−10.8245	−	2.18023i	−0.476522	−	0.0959792i
$517$	−32.8216			−1.44349
$518$			4.02706i			0.176939i
$519$	−21.2203	−	4.27411i	−0.931469	−	0.187613i
$520$	−2.00485	+	3.00952i	−0.0879185	+	0.131976i
$521$			6.31553i			0.276688i	0.990384	+	0.138344i	$0.0441780\pi$
$521$			6.31553i			0.276688i	−0.990384	+	0.138344i	$0.955822\pi$
$522$	12.9455	+	5.43539i	0.566611	+	0.237900i
$523$	−35.7259			−1.56219			−0.781093	−	0.624415i	$-0.785337\pi$
$523$	−35.7259			−1.56219			−0.781093	+	0.624415i	$0.785337\pi$
$524$			4.21104i			0.183960i
$525$	7.16563	−	1.42812i	0.312734	−	0.0623281i
$526$			19.3207i			0.842421i
$527$	−18.8589	−	9.88397i	−0.821506	−	0.430552i
$528$	−4.64398	−	0.935373i	−0.202103	−	0.0407069i
$529$	11.2646			0.489767
$530$	−2.14501	−	1.42894i	−0.0931731	−	0.0620690i
$531$	−3.89128	+	9.26792i	−0.168867	+	0.402193i
$532$			0.657804i			0.0285194i
$533$			12.4705i			0.540157i
$534$	7.06459	+	1.42292i	0.305715	+	0.0615759i
$535$	−1.34390	+	2.01736i	−0.0581019	+	0.0872180i
$536$		−	8.81399i		−	0.380706i
$537$	23.7705	+	4.78777i	1.02577	+	0.206608i
$538$	−21.6216			−0.932172
$539$	17.1985			0.740793
$540$	−10.7603	+	4.38371i	−0.463048	+	0.188645i
$541$	−25.6465			−1.10263			−0.551315	−	0.834297i	$-0.685874\pi$
$541$	−25.6465			−1.10263			−0.551315	+	0.834297i	$0.685874\pi$
$542$		−	26.2479i		−	1.12744i
$543$	4.25941	−	21.1473i	0.182789	−	0.907518i
$544$		−	3.82416i		−	0.163960i
$545$	4.65610	−	6.98936i	0.199445	−	0.299391i
$546$	0.466621	−	2.31670i	0.0199696	−	0.0991457i
$547$		−	26.0653i		−	1.11447i	−0.830354	−	0.557236i	$-0.811862\pi$
$547$		−	26.0653i		−	1.11447i	0.830354	−	0.557236i	$-0.188138\pi$
$548$			4.53024i			0.193522i
$549$	17.7748	−	42.3346i	0.758611	−	1.80680i
$550$	−5.26841	−	12.6197i	−0.224646	−	0.538105i
$551$	−3.64897			−0.155451
$552$	1.17157	−	5.81666i	0.0498653	−	0.247573i
$553$	3.41971			0.145421
$554$	21.4548			0.911529
$555$	13.0851	−	13.0586i	0.555433	−	0.554305i
$556$			4.60841i			0.195440i
$557$			19.0663i			0.807865i	0.914789	+	0.403932i	$0.132357\pi$
$557$			19.0663i			0.807865i	−0.914789	+	0.403932i	$0.867643\pi$
$558$	12.8766	−	10.6392i	0.545110	−	0.450394i
$559$	−10.3097			−0.436053
$560$	−1.57006	−	1.04593i	−0.0663472	−	0.0441984i
$561$	−3.57702	+	17.7593i	−0.151022	+	0.749800i
$562$			4.95539i			0.209030i
$563$	−5.93801			−0.250257			−0.125129	−	0.992141i	$-0.539934\pi$
$563$	−5.93801			−0.250257			−0.125129	+	0.992141i	$0.539934\pi$
$564$	20.3760	+	4.10406i	0.857986	+	0.172812i
$565$	1.36372	−	2.04710i	0.0573720	−	0.0861223i
$566$		−	28.4636i		−	1.19642i
$567$	5.42065	−	5.31725i	0.227646	−	0.223303i
$568$			13.6476i			0.572641i
$569$	−46.4012			−1.94524			−0.972620	−	0.232401i	$-0.925342\pi$
$569$	−46.4012			−1.94524			−0.972620	+	0.232401i	$0.925342\pi$
$570$	2.13740	−	2.13306i	0.0895259	−	0.0893440i
$571$			23.7439i			0.993650i	0.867851	+	0.496825i	$0.165501\pi$
$571$			23.7439i			0.993650i	−0.867851	+	0.496825i	$0.834499\pi$
$572$	−4.42312			−0.184940
$573$	5.20139	−	25.8241i	0.217291	−	1.07882i
$574$	−6.50583			−0.271548
$575$	15.8063	−	6.59876i	0.659170	−	0.275187i
$576$	2.76608	+	1.16138i	0.115253	+	0.0483909i
$577$		−	21.1110i		−	0.878864i	−0.898276	−	0.439432i	$-0.855180\pi$
$577$		−	21.1110i		−	0.878864i	0.898276	−	0.439432i	$-0.144820\pi$
$578$	2.37579			0.0988198
$579$	5.80309	−	28.8114i	0.241168	−	1.19736i
$580$	5.80196	−	8.70944i	0.240913	−	0.361640i
$581$	7.56138			0.313699
$582$	0.191643	−	0.951477i	0.00794385	−	0.0394400i
$583$		−	3.15253i		−	0.130565i
$584$	11.0551			0.457465
$585$	−9.04077	+	5.99618i	−0.373790	+	0.247911i
$586$	−11.1227			−0.459473
$587$		−	24.0595i		−	0.993044i	−0.868024	−	0.496522i	$-0.834610\pi$
$587$		−	24.0595i		−	0.993044i	0.868024	−	0.496522i	$-0.165390\pi$
$588$	−10.6770	−	2.15053i	−0.440314	−	0.0886863i
$589$	−2.01516	+	3.84498i	−0.0830332	+	0.158430i
$590$	6.23522	+	4.15371i	0.256700	+	0.171006i
$591$	0.00944558	−	0.0468958i	0.000388539	−	0.00192904i
$592$	−4.77317			−0.196176
$593$	13.5687			0.557198			0.278599	−	0.960408i	$-0.410130\pi$
$593$	13.5687			0.557198			0.278599	+	0.960408i	$0.410130\pi$
$594$	−11.7593	−	7.98075i	−0.482490	−	0.327454i
$595$	−3.99979	+	6.00416i	−0.163975	+	0.246147i
$596$		−	9.92239i		−	0.406437i
$597$	3.94804	−	19.6014i	0.161582	−	0.802231i
$598$		−	5.54002i		−	0.226548i
$599$		−	6.52509i		−	0.266608i	−0.991075	−	0.133304i	$-0.957441\pi$
$599$		−	6.52509i		−	0.266608i	0.991075	−	0.133304i	$-0.0425586\pi$
$600$	1.69271	+	8.49322i	0.0691045	+	0.346734i
$601$			45.2999i			1.84782i	0.382610	+	0.923910i	$0.375025\pi$
$601$			45.2999i			1.84782i	−0.382610	+	0.923910i	$0.624975\pi$
$602$		−	5.37854i		−	0.219213i
$603$	10.2364	−	24.3802i	0.416859	−	0.992838i
$604$			8.00263i			0.325622i
$605$	−4.36315	+	6.54961i	−0.177387	+	0.266279i
$606$	5.37012	−	26.6618i	0.218146	−	1.08306i
$607$			33.6927i			1.36755i	0.729695	+	0.683773i	$0.239662\pi$
$607$			33.6927i			1.36755i	−0.729695	+	0.683773i	$0.760338\pi$
$608$	−0.779676			−0.0316200
$609$	−1.35038	+	6.70445i	−0.0547203	+	0.271678i
$610$	−28.4816	−	18.9736i	−1.15319	−	0.768218i
$611$	19.4070			0.785121
$612$	4.44131	−	10.5779i	0.179529	−	0.427588i
$613$	46.1698			1.86478			0.932391	−	0.361452i	$-0.117719\pi$
$613$	46.1698			1.86478			0.932391	+	0.361452i	$0.117719\pi$
$614$		−	1.52502i		−	0.0615447i
$615$	21.0964	+	21.1394i	0.850690	+	0.852422i
$616$		−	2.30753i		−	0.0929730i
$617$	−34.5419			−1.39061			−0.695303	−	0.718717i	$-0.744730\pi$
$617$	−34.5419			−1.39061			−0.695303	+	0.718717i	$0.744730\pi$
$618$	3.83827	−	19.0564i	0.154398	−	0.766561i
$619$		−	46.6397i		−	1.87461i	−0.348513	−	0.937304i	$-0.613313\pi$
$619$		−	46.6397i		−	1.87461i	0.348513	−	0.937304i	$-0.386687\pi$
$620$	−5.97313	−	10.9235i	−0.239887	−	0.438696i
$621$	9.99601	−	14.7287i	0.401126	−	0.591042i
$622$			9.63822i			0.386457i
$623$			3.51030i			0.140637i
$624$	2.74592	+	0.553073i	0.109925	+	0.0221407i
$625$	−17.5791	+	17.7757i	−0.703163	+	0.711029i
$626$	1.15835			0.0462971
$627$	3.62080	+	0.729288i	0.144601	+	0.0291250i
$628$		−	3.59827i		−	0.143586i
$629$			18.2534i			0.727809i
$630$	−3.12819	−	4.71655i	−0.124630	−	0.187912i
$631$		−	32.0076i		−	1.27420i	−0.770779	−	0.637102i	$-0.780133\pi$
$631$		−	32.0076i		−	1.27420i	0.770779	−	0.637102i	$-0.219867\pi$
$632$			4.05329i			0.161231i
$633$	30.8155	+	6.20674i	1.22481	+	0.246696i
$634$	28.4993			1.13185
$635$	7.03838	−	10.5655i	0.279310	−	0.419277i
$636$	−0.394197	+	1.95713i	−0.0156309	+	0.0776052i
$637$	−10.1692			−0.402920
$638$	12.8003			0.506770
$639$	−15.8501	+	37.7504i	−0.627020	+	1.49338i
$640$	1.23971	−	1.86095i	0.0490037	−	0.0735604i
$641$	−19.2820			−0.761595			−0.380797	−	0.924659i	$-0.624350\pi$
$641$	−19.2820			−0.761595			−0.380797	+	0.924659i	$0.624350\pi$
$642$	1.84066	+	0.370739i	0.0726451	+	0.0146319i
$643$	−25.2374			−0.995266			−0.497633	−	0.867388i	$-0.665797\pi$
$643$	−25.2374			−0.995266			−0.497633	+	0.867388i	$0.665797\pi$
$644$	2.89021			0.113890
$645$	−17.4765	+	17.4410i	−0.688136	+	0.686738i
$646$			2.98161i			0.117310i
$647$		−	22.7073i		−	0.892716i	−0.894854	−	0.446358i	$-0.852721\pi$
$647$		−	22.7073i		−	0.892716i	0.894854	−	0.446358i	$-0.147279\pi$
$648$	6.30239	+	6.42495i	0.247581	+	0.252396i
$649$			9.16395i			0.359717i
$650$	3.11514	+	7.46184i	0.122186	+	0.292678i
$651$	6.31884	+	5.12549i	0.247655	+	0.200884i
$652$		−	5.86145i		−	0.229552i
$653$	15.1565			0.593118			0.296559	−	0.955014i	$-0.404161\pi$
$653$	15.1565			0.593118			0.296559	+	0.955014i	$0.404161\pi$
$654$	−6.37718	−	1.28447i	−0.249367	−	0.0502266i
$655$	7.83653	+	5.22045i	0.306199	+	0.203980i
$656$		−	7.71117i		−	0.301071i
$657$	30.5794	+	12.8392i	1.19302	+	0.500906i
$658$			10.1246i			0.394697i
$659$			8.23517i			0.320797i	0.987052	+	0.160398i	$0.0512779\pi$
$659$			8.23517i			0.320797i	−0.987052	+	0.160398i	$0.948722\pi$
$660$	−7.49786	+	7.48262i	−0.291854	+	0.291261i
$661$	43.4313			1.68928			0.844641	−	0.535333i	$-0.179814\pi$
$661$	43.4313			1.68928			0.844641	+	0.535333i	$0.179814\pi$
$662$		−	24.7211i		−	0.960815i
$663$	2.11504	−	10.5009i	0.0821414	−	0.407819i
$664$			8.96229i			0.347804i
$665$	1.22414	+	0.815483i	0.0474701	+	0.0316231i
$666$	−13.2030	−	5.54347i	−0.511604	−	0.214805i
$667$			16.0326i			0.620785i
$668$			18.7631i			0.725966i
$669$	−30.4424	−	6.13158i	−1.17697	−	0.237061i
$670$	−16.4024	−	10.9268i	−0.633679	−	0.422137i
$671$		−	41.8597i		−	1.61598i
$672$	−0.288537	+	1.43254i	−0.0111306	+	0.0552615i
$673$	9.05937			0.349213			0.174607	−	0.984638i	$-0.444135\pi$
$673$	9.05937			0.349213			0.174607	+	0.984638i	$0.444135\pi$
$674$	−21.0103			−0.809285
$675$	−5.18170	+	25.4588i	−0.199444	+	0.979909i
$676$	−10.3847			−0.399410
$677$		−	31.3879i		−	1.20634i	−0.797614	−	0.603168i	$-0.793905\pi$
$677$		−	31.3879i		−	1.20634i	0.797614	−	0.603168i	$-0.206095\pi$
$678$	−1.86780	−	0.376206i	−0.0717325	−	0.0144481i
$679$	0.472776			0.0181435
$680$	−7.11657	−	4.74084i	−0.272908	−	0.181803i
$681$	−0.299623	−	0.0603488i	−0.0114816	−	0.00231257i
$682$	7.06904	−	13.4879i	0.270688	−	0.516479i
$683$	−28.6914			−1.09785			−0.548923	−	0.835873i	$-0.684962\pi$
$683$	−28.6914			−1.09785			−0.548923	+	0.835873i	$0.684962\pi$
$684$	−2.15665	−	0.905502i	−0.0824614	−	0.0346227i
$685$	8.43055	+	5.61617i	0.322115	+	0.214583i
$686$		−	11.2111i		−	0.428041i
$687$	3.78395	−	18.7867i	0.144367	−	0.716758i
$688$	6.37503			0.243046
$689$			1.86405i			0.0710146i
$690$	−9.37210	−	9.39117i	−0.356790	−	0.357516i
$691$	1.01732			0.0387008			0.0193504	−	0.999813i	$-0.493840\pi$
$691$	1.01732			0.0387008			0.0193504	+	0.999813i	$0.493840\pi$
$692$	12.4976			0.475087
$693$	2.67992	−	6.38281i	0.101802	−	0.242463i
$694$		−	0.887639i		−	0.0336943i
$695$	8.57601	+	5.71308i	0.325307	+	0.216709i
$696$	−7.94659	−	1.60057i	−0.301215	−	0.0606695i
$697$	−29.4888			−1.11697
$698$	−15.6359			−0.591827
$699$	−41.1280	−	8.28384i	−1.55560	−	0.313323i
$700$	−3.89283	+	1.62516i	−0.147135	+	0.0614253i
$701$		−	34.7599i		−	1.31286i	−0.754385	−	0.656432i	$-0.772065\pi$
$701$		−	34.7599i		−	1.31286i	0.754385	−	0.656432i	$-0.227935\pi$
$702$	6.95311	+	4.71891i	0.262428	+	0.178104i
$703$	3.72152			0.140360
$704$	2.73505			0.103081
$705$	32.8977	−	32.8309i	1.23900	−	1.23648i
$706$			28.4457i			1.07057i
$707$	13.2479			0.498238
$708$	1.14587	−	5.68909i	0.0430646	−	0.213809i
$709$		−	37.7590i		−	1.41807i	−0.705174	−	0.709034i	$-0.749131\pi$
$709$		−	37.7590i		−	1.41807i	0.705174	−	0.709034i	$-0.250869\pi$
$710$	25.3975	+	16.9190i	0.953151	+	0.634960i
$711$	−4.70741	+	11.2117i	−0.176542	+	0.420472i
$712$	−4.16066			−0.155927
$713$	16.8938	+	8.85408i	0.632679	+	0.331588i
$714$	5.47827	+	1.10341i	0.205019	+	0.0412942i
$715$	−5.48336	+	8.23119i	−0.205066	+	0.307829i
$716$	−13.9995			−0.523187
$717$	−29.8872	−	6.01977i	−1.11616	−	0.224812i
$718$		−	19.6674i		−	0.733982i
$719$	38.8477			1.44877			0.724387	−	0.689393i	$-0.242123\pi$
$719$	38.8477			1.44877			0.724387	+	0.689393i	$0.242123\pi$
$720$	5.59040	−	3.70776i	0.208342	−	0.138180i
$721$	9.46886			0.352639
$722$	−18.3921			−0.684483
$723$	0.711848	−	3.53422i	0.0264739	−	0.131439i
$724$			12.4546i			0.462871i
$725$	−9.01509	−	21.5943i	−0.334812	−	0.801991i
$726$	5.97594	+	1.20365i	0.221788	+	0.0446717i
$727$			29.4589i			1.09257i	0.837600	+	0.546284i	$0.183958\pi$
$727$			29.4589i			1.09257i	−0.837600	+	0.546284i	$0.816042\pi$
$728$			1.36441i			0.0505684i
$729$	9.97108	+	25.0914i	0.369299	+	0.929310i
$730$	13.7051	−	20.5730i	0.507249	−	0.761442i
$731$		−	24.3792i		−	0.901696i
$732$	−5.23420	+	25.9870i	−0.193462	+	0.960507i
$733$			2.97820i			0.110002i	0.998486	+	0.0550011i	$0.0175162\pi$
$733$			2.97820i			0.110002i	−0.998486	+	0.0550011i	$0.982484\pi$
$734$	11.1028			0.409813
$735$	−17.2384	+	17.2034i	−0.635849	+	0.634557i
$736$			3.42569i			0.126273i
$737$		−	24.1067i		−	0.887982i
$738$	8.95561	−	21.3297i	0.329661	−	0.785158i
$739$			26.3511i			0.969341i	0.874697	+	0.484671i	$0.161061\pi$
$739$			26.3511i			0.969341i	−0.874697	+	0.484671i	$0.838939\pi$
$740$	−5.91732	+	8.88262i	−0.217525	+	0.326531i
$741$	−2.14093	−	0.431218i	−0.0786491	−	0.0158412i
$742$	−0.972470			−0.0357005
$743$			37.7660i			1.38550i	0.721177	+	0.692751i	$0.243601\pi$
$743$			37.7660i			1.38550i	−0.721177	+	0.692751i	$0.756399\pi$
$744$	−6.07510	+	7.48954i	−0.222724	+	0.274580i
$745$	−18.4651	−	12.3008i	−0.676507	−	0.450668i
$746$			9.10716i			0.333437i
$747$	−10.4086	+	24.7904i	−0.380832	+	0.907034i
$748$		−	10.4593i		−	0.382429i
$749$			0.914599i			0.0334187i
$750$	17.9039	+	7.37905i	0.653758	+	0.269445i
$751$	−48.5906			−1.77310			−0.886549	−	0.462635i	$-0.846904\pi$
$751$	−48.5906			−1.77310			−0.886549	+	0.462635i	$0.846904\pi$
$752$	−12.0004			−0.437608
$753$	−12.0311	−	2.42326i	−0.438438	−	0.0883086i
$754$	−7.56866			−0.275634
$755$	14.8925	+	9.92090i	0.541993	+	0.361059i
$756$	−2.46184	+	3.62742i	−0.0895364	+	0.131928i
$757$	28.1542			1.02328			0.511642	−	0.859199i	$-0.329038\pi$
$757$	28.1542			1.02328			0.511642	+	0.859199i	$0.329038\pi$
$758$	16.6992			0.606541
$759$	3.20430	−	15.9088i	0.116309	−	0.577455i
$760$	−0.966569	+	1.45094i	−0.0350612	+	0.0526310i
$761$	−12.1196			−0.439337			−0.219668	−	0.975575i	$-0.570498\pi$
$761$	−12.1196			−0.439337			−0.219668	+	0.975575i	$0.570498\pi$
$762$	−9.64005	−	1.94166i	−0.349222	−	0.0703390i
$763$		−	3.16873i		−	0.114716i
$764$			15.2090i			0.550241i
$765$	−14.1791	−	21.3786i	−0.512645	−	0.772944i
$766$			2.67292i			0.0965764i
$767$		−	5.41852i		−	0.195651i
$768$	−1.69795	−	0.341995i	−0.0612695	−	0.0123407i
$769$	27.9794			1.00896			0.504481	−	0.863423i	$-0.331684\pi$
$769$	27.9794			1.00896			0.504481	+	0.863423i	$0.331684\pi$
$770$	−4.29419	−	2.86066i	−0.154752	−	0.103091i
$771$	−38.8697	−	7.82898i	−1.39986	−	0.281954i
$772$			16.9683i			0.610704i
$773$			42.4045i			1.52518i	0.646880	+	0.762592i	$0.276074\pi$
$773$			42.4045i			1.52518i	−0.646880	+	0.762592i	$0.723926\pi$
$774$	17.6338	+	7.40385i	0.633835	+	0.266126i
$775$	−27.7329	−	2.42619i	−0.996195	−	0.0871513i
$776$			0.560368i			0.0201160i
$777$	1.37724	−	6.83776i	0.0494080	−	0.245303i
$778$	−4.87027			−0.174608
$779$			6.01222i			0.215410i
$780$	4.43338	−	4.42437i	0.158740	−	0.158418i
$781$			37.3269i			1.33566i
$782$	13.1004			0.468469
$783$	−20.1220	−	13.6563i	−0.719103	−	0.488038i
$784$	6.28819			0.224578
$785$	−6.69619	−	4.46079i	−0.238997	−	0.159212i
$786$	1.44015	−	7.15014i	0.0513686	−	0.255037i
$787$	8.79175			0.313392			0.156696	−	0.987647i	$-0.449916\pi$
$787$	8.79175			0.313392			0.156696	+	0.987647i	$0.449916\pi$
$788$			0.0276191i			0.000983889i
$789$	6.60757	−	32.8055i	0.235236	−	1.16791i
$790$	7.54296	+	5.02488i	0.268366	+	0.178777i
$791$		−	0.928085i		−	0.0329989i
$792$	7.56537	+	3.17644i	0.268824	+	0.112870i
$793$			24.7511i			0.878936i
$794$		−	30.4343i		−	1.08007i
$795$	3.15343	+	3.15985i	0.111841	+	0.112068i
$796$			11.5441i			0.409171i
$797$			45.0253i			1.59488i	0.603400	+	0.797439i	$0.293812\pi$
$797$			45.0253i			1.59488i	−0.603400	+	0.797439i	$0.706188\pi$
$798$	0.224965	−	1.11692i	0.00796369	−	0.0395385i
$799$			45.8913i			1.62352i
$800$	−1.92626	−	4.61406i	−0.0681035	−	0.163132i
$801$	−11.5087	−	4.83211i	−0.406640	−	0.170734i
$802$	−6.28004			−0.221756
$803$	30.2364			1.06702
$804$	−3.01434	+	14.9657i	−0.106308	+	0.527801i
$805$	3.58302	−	5.37854i	0.126285	−	0.189569i
$806$	−4.17983	+	7.97522i	−0.147228	+	0.280915i
$807$	36.7124	+	7.39446i	1.29234	+	0.260297i
$808$			15.7023i			0.552406i
$809$	35.1700			1.23651			0.618256	−	0.785977i	$-0.287839\pi$
$809$	35.1700			1.23651			0.618256	+	0.785977i	$0.287839\pi$
$810$	19.7696	−	3.76337i	0.694633	−	0.132231i
$811$	−22.8205			−0.801335			−0.400667	−	0.916224i	$-0.631222\pi$
$811$	−22.8205			−0.801335			−0.400667	+	0.916224i	$0.631222\pi$
$812$		−	3.94855i		−	0.138567i
$813$	−8.97665	+	44.5677i	−0.314825	+	1.56306i
$814$	−13.0548			−0.457572
$815$	−10.9078	−	7.26647i	−0.382085	−	0.254533i
$816$	−1.30784	+	6.49324i	−0.0457837	+	0.227309i
$817$	−4.97046			−0.173894
$818$		−	0.893121i		−	0.0312272i
$819$	−1.58460	+	3.77407i	−0.0553704	+	0.131877i
$820$	−14.3501	−	9.55959i	−0.501127	−	0.333835i
$821$	−11.3872			−0.397417			−0.198708	−	0.980059i	$-0.563675\pi$
$821$	−11.3872			−0.397417			−0.198708	+	0.980059i	$0.563675\pi$
$822$	1.54932	−	7.69213i	0.0540387	−	0.268294i
$823$	−45.1246			−1.57295			−0.786473	−	0.617625i	$-0.788095\pi$
$823$	−45.1246			−1.57295			−0.786473	+	0.617625i	$0.788095\pi$
$824$			11.2232i			0.390978i
$825$	4.62964	+	23.2294i	0.161183	+	0.808743i
$826$	2.82683			0.0983579
$827$		−	37.7917i		−	1.31415i	−0.753827	−	0.657073i	$-0.771795\pi$
$827$		−	37.7917i		−	1.31415i	0.753827	−	0.657073i	$-0.228205\pi$
$828$	−3.97853	+	9.47573i	−0.138264	+	0.329304i
$829$		−	36.3927i		−	1.26397i	−0.774981	−	0.631985i	$-0.782240\pi$
$829$		−	36.3927i		−	1.26397i	0.774981	−	0.631985i	$-0.217760\pi$
$830$	16.6784	+	11.1106i	0.578915	+	0.385655i
$831$	−36.4293	−	7.33744i	−1.26372	−	0.254533i
$832$	−1.61720			−0.0560662
$833$		−	24.0471i		−	0.833181i
$834$	1.57605	−	7.82486i	0.0545743	−	0.270953i
$835$	34.9172	+	23.2607i	1.20836	+	0.804971i
$836$	−2.13245			−0.0737524
$837$	−25.5024	+	13.6612i	−0.881492	+	0.472199i
$838$		−	8.98602i		−	0.310417i
$839$			50.5974i			1.74682i	0.486988	+	0.873409i	$0.338096\pi$
$839$			50.5974i			1.74682i	−0.486988	+	0.873409i	$0.661904\pi$
$840$	2.30818	+	2.31288i	0.0796399	+	0.0798021i
$841$	−7.09661			−0.244711
$842$	25.5348			0.879986
$843$	1.69472	−	8.41400i	0.0583691	−	0.289794i
$844$	−18.1486			−0.624701
$845$	−12.8739	+	19.3253i	−0.442877	+	0.664812i
$846$	−33.1939	−	13.9370i	−1.14123	−	0.479164i
$847$			2.96936i			0.102028i
$848$		−	1.15264i		−	0.0395819i
$849$	−9.73442	+	48.3299i	−0.334084	+	1.65868i
$850$	−17.6449	+	7.36632i	−0.605215	+	0.252663i
$851$		−	16.3514i		−	0.560518i
$852$	4.66741	−	23.1730i	0.159903	−	0.793894i
$853$			44.0138i			1.50701i	0.657445	+	0.753503i	$0.271637\pi$
$853$			44.0138i			1.50701i	−0.657445	+	0.753503i	$0.728363\pi$
$854$	−12.9126			−0.441859
$855$	−4.35870	+	2.89085i	−0.149064	+	0.0988650i
$856$	−1.08405			−0.0370520
$857$	−6.50550			−0.222224			−0.111112	−	0.993808i	$-0.535441\pi$
$857$	−6.50550			−0.222224			−0.111112	+	0.993808i	$0.535441\pi$
$858$	7.51024	+	1.51268i	0.256395	+	0.0516422i
$859$		−	19.1458i		−	0.653248i	−0.945154	−	0.326624i	$-0.894089\pi$
$859$		−	19.1458i		−	0.653248i	0.945154	−	0.326624i	$-0.105911\pi$
$860$	7.90317	−	11.8636i	0.269496	−	0.404546i
$861$	11.0466	+	2.22496i	0.376466	+	0.0758264i
$862$			14.8006i			0.504109i
$863$		−	41.1273i		−	1.39999i	−0.714148	−	0.699995i	$-0.753186\pi$
$863$		−	41.1273i		−	1.39999i	0.714148	−	0.699995i	$-0.246814\pi$
$864$	−4.29948	−	2.91795i	−0.146271	−	0.0992708i
$865$	15.4933	−	23.2574i	0.526790	−	0.790775i
$866$	−29.4170			−0.999631
$867$	−4.03398	−	0.812508i	−0.137001	−	0.0275942i
$868$	−4.16066	−	2.18061i	−0.141222	−	0.0740146i
$869$			11.0859i			0.376065i
$870$	−12.8300	+	12.8040i	−0.434979	+	0.434095i
$871$			14.2540i			0.482977i
$872$	3.75581			0.127188
$873$	−0.650801	+	1.55002i	−0.0220263	+	0.0524603i
$874$		−	2.67093i		−	0.0903455i
$875$	−1.80162	+	9.25907i	−0.0609059	+	0.313014i
$876$	−18.7711	−	3.78080i	−0.634216	−	0.127741i
$877$			21.2843i			0.718720i	0.933199	+	0.359360i	$0.117005\pi$
$877$			21.2843i			0.718720i	−0.933199	+	0.359360i	$0.882995\pi$
$878$	19.6199			0.662139
$879$	18.8857	+	3.80389i	0.637000	+	0.128302i
$880$	3.39066	−	5.08979i	0.114299	−	0.171577i
$881$	29.3023			0.987218			0.493609	−	0.869684i	$-0.335677\pi$
$881$	29.3023			0.987218			0.493609	+	0.869684i	$0.335677\pi$
$882$	17.3936	+	7.30299i	0.585674	+	0.245904i
$883$	24.5692			0.826818			0.413409	−	0.910545i	$-0.364338\pi$
$883$	24.5692			0.826818			0.413409	+	0.910545i	$0.364338\pi$
$884$			6.18442i			0.208005i
$885$	−9.16655	−	9.18521i	−0.308130	−	0.308758i
$886$	3.60874			0.121238
$887$	−41.9216			−1.40759			−0.703794	−	0.710404i	$-0.748512\pi$
$887$	−41.9216			−1.40759			−0.703794	+	0.710404i	$0.748512\pi$
$888$	8.10460	+	1.63240i	0.271973	+	0.0547797i
$889$		−	4.79000i		−	0.160652i
$890$	−5.15799	+	7.74277i	−0.172896	+	0.259538i
$891$	17.2373	+	17.5726i	0.577473	+	0.588703i
$892$	17.9289			0.600303
$893$	9.35639			0.313100
$894$	−3.39341	+	16.8477i	−0.113492	+	0.563473i
$895$	−17.3553	+	26.0524i	−0.580124	+	0.870837i
$896$		−	0.843688i		−	0.0281856i
$897$	−1.89466	+	9.40668i	−0.0632608	+	0.314080i
$898$	2.43366			0.0812123
$899$	12.0963	−	23.0800i	0.403433	−	0.769761i
$900$	0.0305023	−	15.0000i	0.00101674	−	0.499999i
$901$	−4.40789			−0.146848
$902$		−	21.0904i		−	0.702235i
$903$	−1.83943	+	9.13250i	−0.0612125	+	0.303911i
$904$	1.10003			0.0365865
$905$	23.1774	+	15.4400i	0.770441	+	0.513244i
$906$	2.73686	−	13.5881i	0.0909260	−	0.451433i
$907$			1.36753i			0.0454080i	0.999742	+	0.0227040i	$0.00722752\pi$
$907$			1.36753i			0.0454080i	−0.999742	+	0.0227040i	$0.992772\pi$
$908$	0.176461			0.00585607
$909$	−18.2364	+	43.4339i	−0.604863	+	1.44061i
$910$	2.53910	+	1.69147i	0.0841703	+	0.0560716i
$911$	41.6059			1.37847			0.689233	−	0.724540i	$-0.257948\pi$
$911$	41.6059			1.37847			0.689233	+	0.724540i	$0.257948\pi$
$912$	1.32385	+	0.266645i	0.0438371	+	0.00882951i
$913$			24.5123i			0.811240i
$914$	−3.07246			−0.101628
$915$	41.8716	+	41.9568i	1.38423	+	1.38705i
$916$			11.0643i			0.365576i
$917$	3.55281			0.117324
$918$	−11.1587	+	16.4419i	−0.368293	+	0.542664i
$919$	−51.3896			−1.69519			−0.847593	−	0.530647i	$-0.821949\pi$
$919$	−51.3896			−1.69519			−0.847593	+	0.530647i	$0.821949\pi$
$920$	6.37503	+	4.24685i	0.210179	+	0.140014i
$921$	−0.521548	+	2.58940i	−0.0171856	+	0.0853238i
$922$	−33.4920			−1.10300
$923$		−	22.0709i		−	0.726472i
$924$	−0.789163	+	3.91807i	−0.0259616	+	0.128895i
$925$	9.19435	+	22.0237i	0.302308	+	0.724134i
$926$	−21.3313			−0.700989
$927$	−13.0344	+	31.0442i	−0.428106	+	1.01963i
$928$	4.68011			0.153632
$929$	34.3799			1.12797			0.563983	−	0.825786i	$-0.309268\pi$
$929$	34.3799			1.12797			0.563983	+	0.825786i	$0.309268\pi$
$930$	6.40631	+	20.5903i	0.210071	+	0.675181i
$931$	−4.90275			−0.160681
$932$	24.2221			0.793421
$933$	3.29622	−	16.3652i	0.107913	−	0.535773i
$934$	−4.43260			−0.145039
$935$	−19.4642	−	12.9664i	−0.636546	−	0.424047i
$936$	−4.47330	−	1.87818i	−0.146214	−	0.0613903i
$937$		−	32.4420i		−	1.05983i	−0.848050	−	0.529916i	$-0.822223\pi$
$937$		−	32.4420i		−	1.05983i	0.848050	−	0.529916i	$-0.177777\pi$
$938$	−7.43626			−0.242802
$939$	−1.96683	−	0.396150i	−0.0641849	−	0.0129279i
$940$	−14.8769	+	22.3320i	−0.485232	+	0.728391i
$941$	34.1816			1.11429			0.557145	−	0.830415i	$-0.311897\pi$
$941$	34.1816			1.11429			0.557145	+	0.830415i	$0.311897\pi$
$942$	−1.23059	+	6.10968i	−0.0400947	+	0.199064i
$943$	26.4161			0.860226
$944$			3.35056i			0.109051i
$945$	3.69848	+	9.07830i	0.120312	+	0.295317i
$946$	17.4360			0.566894
$947$		−	2.99592i		−	0.0973544i	−0.998815	−	0.0486772i	$-0.984499\pi$
$947$		−	2.99592i		−	0.0973544i	0.998815	−	0.0486772i	$-0.0155006\pi$
$948$	1.38620	−	6.88228i	0.0450218	−	0.223526i
$949$	−17.8783			−0.580356
$950$	1.50186	+	3.59747i	0.0487267	+	0.116717i
$951$	−48.3905	−	9.74662i	−1.56917	−	0.316056i
$952$	−3.22640			−0.104568
$953$			48.2109i			1.56170i	0.624716	+	0.780852i	$0.285215\pi$
$953$			48.2109i			1.56170i	−0.624716	+	0.780852i	$0.714785\pi$
$954$	1.33866	−	3.18830i	0.0433406	−	0.103225i
$955$	28.3031	+	18.8547i	0.915867	+	0.610122i
$956$	17.6019			0.569287
$957$	−21.7343	−	4.37765i	−0.702571	−	0.141509i
$958$			3.79781i			0.122702i
$959$	3.82211			0.123422
$960$	−2.74140	+	2.73583i	−0.0884782	+	0.0882984i
$961$	−17.6396	−	25.4921i	−0.569018	−	0.822325i
$962$	7.71915			0.248875
$963$	−2.99856	−	1.25899i	−0.0966274	−	0.0405705i
$964$			2.08146i			0.0670393i
$965$	31.5772	+	21.0358i	1.01651	+	0.677165i
$966$	−4.90744	−	0.988439i	−0.157894	−	0.0318025i
$967$	8.15782			0.262338			0.131169	−	0.991360i	$-0.458127\pi$
$967$	8.15782			0.262338			0.131169	+	0.991360i	$0.458127\pi$
$968$	−3.51950			−0.113121
$969$	1.01969	−	5.06263i	0.0327573	−	0.162635i
$970$	1.04282	+	0.694691i	0.0334828	+	0.0223052i
$971$		−	57.7334i		−	1.85275i	−0.376600	−	0.926376i	$-0.622907\pi$
$971$		−	57.7334i		−	1.85275i	0.376600	−	0.926376i	$-0.377093\pi$
$972$	−8.50385	−	13.0646i	−0.272761	−	0.419048i
$973$	3.88806			0.124646
$974$	−19.3169			−0.618953
$975$	−2.73744	−	13.7352i	−0.0876683	−	0.439879i
$976$		−	15.3049i		−	0.489898i
$977$	−29.8461			−0.954861			−0.477430	−	0.878670i	$-0.658432\pi$
$977$	−29.8461			−0.954861			−0.477430	+	0.878670i	$0.658432\pi$
$978$	−2.00458	+	9.95245i	−0.0640995	+	0.318244i
$979$	−11.3796			−0.363694
$980$	7.79551	−	11.7020i	0.249018	−	0.373807i
$981$	10.3889	+	4.36193i	0.331691	+	0.139266i
$982$	4.82700			0.154036
$983$			38.4653i			1.22685i	0.789752	+	0.613426i	$0.210209\pi$
$983$			38.4653i			1.22685i	−0.789752	+	0.613426i	$0.789791\pi$
$984$	−2.63718	+	13.0932i	−0.0840703	+	0.417396i
$985$	0.0513977	+	0.0342395i	0.00163767	+	0.00109096i
$986$		−	17.8975i		−	0.569972i
$987$	3.46255	−	17.1910i	0.110214	−	0.547196i
$988$	1.26089			0.0401143
$989$			21.8389i			0.694436i
$990$	15.2900	−	10.1409i	0.485949	−	0.322299i
$991$		−	47.2705i		−	1.50160i	−0.660531	−	0.750799i	$-0.729669\pi$
$991$		−	47.2705i		−	1.50160i	0.660531	−	0.750799i	$-0.270331\pi$
$992$	2.58461	−	4.93151i	0.0820615	−	0.156576i
$993$	−8.45451	+	41.9753i	−0.268296	+	1.33205i
$994$	11.5143			0.365212
$995$	21.4830	+	14.3113i	0.681058	+	0.453700i
$996$	3.06506	−	15.2175i	0.0971201	−	0.482186i
$997$			32.1841i			1.01928i	0.860387	+	0.509640i	$0.170222\pi$
$997$			32.1841i			1.01928i	−0.860387	+	0.509640i	$0.829778\pi$
$998$			43.7159i			1.38380i
$999$	20.5221	+	13.9279i	0.649292	+	0.440659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.e.b.929.3	yes	32
3.2	odd	2		930.2.e.a.929.4	yes	32
5.4	even	2		930.2.e.a.929.30	yes	32
15.14	odd	2	inner	930.2.e.b.929.29	yes	32
31.30	odd	2	inner	930.2.e.b.929.30	yes	32
93.92	even	2		930.2.e.a.929.29	yes	32
155.154	odd	2		930.2.e.a.929.3	✓	32
465.464	even	2	inner	930.2.e.b.929.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.e.a.929.3	✓	32	155.154	odd	2
930.2.e.a.929.4	yes	32	3.2	odd	2
930.2.e.a.929.29	yes	32	93.92	even	2
930.2.e.a.929.30	yes	32	5.4	even	2
930.2.e.b.929.3	yes	32	1.1	even	1	trivial
930.2.e.b.929.4	yes	32	465.464	even	2	inner
930.2.e.b.929.29	yes	32	15.14	odd	2	inner
930.2.e.b.929.30	yes	32	31.30	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.69795 - 0.341995i) q^{3} +1.00000 q^{4} +(1.23971 - 1.86095i) q^{5} +(-1.69795 - 0.341995i) q^{6} -0.843688i q^{7} +1.00000 q^{8} +(2.76608 + 1.16138i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.69795 - 0.341995i) q^{3} +1.00000 q^{4} +(1.23971 - 1.86095i) q^{5} +(-1.69795 - 0.341995i) q^{6} -0.843688i q^{7} +1.00000 q^{8} +(2.76608 + 1.16138i) q^{9} +(1.23971 - 1.86095i) q^{10} +2.73505 q^{11} +(-1.69795 - 0.341995i) q^{12} -1.61720 q^{13} -0.843688i q^{14} +(-2.74140 + 2.73583i) q^{15} +1.00000 q^{16} -3.82416i q^{17} +(2.76608 + 1.16138i) q^{18} -0.779676 q^{19} +(1.23971 - 1.86095i) q^{20} +(-0.288537 + 1.43254i) q^{21} +2.73505 q^{22} +3.42569i q^{23} +(-1.69795 - 0.341995i) q^{24} +(-1.92626 - 4.61406i) q^{25} -1.61720 q^{26} +(-4.29948 - 2.91795i) q^{27} -0.843688i q^{28} +4.68011 q^{29} +(-2.74140 + 2.73583i) q^{30} +(2.58461 - 4.93151i) q^{31} +1.00000 q^{32} +(-4.64398 - 0.935373i) q^{33} -3.82416i q^{34} +(-1.57006 - 1.04593i) q^{35} +(2.76608 + 1.16138i) q^{36} -4.77317 q^{37} -0.779676 q^{38} +(2.74592 + 0.553073i) q^{39} +(1.23971 - 1.86095i) q^{40} -7.71117i q^{41} +(-0.288537 + 1.43254i) q^{42} +6.37503 q^{43} +2.73505 q^{44} +(5.59040 - 3.70776i) q^{45} +3.42569i q^{46} -12.0004 q^{47} +(-1.69795 - 0.341995i) q^{48} +6.28819 q^{49} +(-1.92626 - 4.61406i) q^{50} +(-1.30784 + 6.49324i) q^{51} -1.61720 q^{52} -1.15264i q^{53} +(-4.29948 - 2.91795i) q^{54} +(3.39066 - 5.08979i) q^{55} -0.843688i q^{56} +(1.32385 + 0.266645i) q^{57} +4.68011 q^{58} +3.35056i q^{59} +(-2.74140 + 2.73583i) q^{60} -15.3049i q^{61} +(2.58461 - 4.93151i) q^{62} +(0.979844 - 2.33371i) q^{63} +1.00000 q^{64} +(-2.00485 + 3.00952i) q^{65} +(-4.64398 - 0.935373i) q^{66} -8.81399i q^{67} -3.82416i q^{68} +(1.17157 - 5.81666i) q^{69} +(-1.57006 - 1.04593i) q^{70} +13.6476i q^{71} +(2.76608 + 1.16138i) q^{72} +11.0551 q^{73} -4.77317 q^{74} +(1.69271 + 8.49322i) q^{75} -0.779676 q^{76} -2.30753i q^{77} +(2.74592 + 0.553073i) q^{78} +4.05329i q^{79} +(1.23971 - 1.86095i) q^{80} +(6.30239 + 6.42495i) q^{81} -7.71117i q^{82} +8.96229i q^{83} +(-0.288537 + 1.43254i) q^{84} +(-7.11657 - 4.74084i) q^{85} +6.37503 q^{86} +(-7.94659 - 1.60057i) q^{87} +2.73505 q^{88} -4.16066 q^{89} +(5.59040 - 3.70776i) q^{90} +1.36441i q^{91} +3.42569i q^{92} +(-6.07510 + 7.48954i) q^{93} -12.0004 q^{94} +(-0.966569 + 1.45094i) q^{95} +(-1.69795 - 0.341995i) q^{96} +0.560368i q^{97} +6.28819 q^{98} +(7.56537 + 3.17644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9	\( 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} + 4 q^{18} + 8 q^{19} - 2 q^{20} + 10 q^{25} - 12 q^{31} + 32 q^{32} + 8 q^{33} - 16 q^{35} + 4 q^{36} + 8 q^{38} - 4 q^{39} - 2 q^{40} - 42 q^{45} + 4 q^{47} - 36 q^{49} + 10 q^{50} - 4 q^{51} - 12 q^{62} + 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} + 4 q^{72} + 8 q^{76} - 4 q^{78} - 2 q^{80} + 24 q^{81} + 4 q^{87} - 42 q^{90} - 24 q^{93} + 4 q^{94} + 26 q^{95} - 36 q^{98}+O(q^{100}) \) 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 + 4 * q^18 + 8 * q^19 - 2 * q^20 + 10 * q^25 - 12 * q^31 + 32 * q^32 + 8 * q^33 - 16 * q^35 + 4 * q^36 + 8 * q^38 - 4 * q^39 - 2 * q^40 - 42 * q^45 + 4 * q^47 - 36 * q^49 + 10 * q^50 - 4 * q^51 - 12 * q^62 + 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 + 4 * q^72 + 8 * q^76 - 4 * q^78 - 2 * q^80 + 24 * q^81 + 4 * q^87 - 42 * q^90 - 24 * q^93 + 4 * q^94 + 26 * q^95 - 36 * q^98

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